Question

Is log2 rational ? Justify
your
answer ?​

Answer 1

Answer:

No it is not..............................

Answer 2

Answer:

Log2 is irrational.

Step-by-step explanation:

Assume that log 2 is rational, that is,

log2 = p/q ......(1)

where p, q are integers.

Since log 1 = 0 and log 10 = 1, 0 < log 2 < 1 and therefore p < q.

From (1),

2= 10^(p/q)

2^q=(2×5)^p

2(p-q)=5^p

where q – p is an integer greater than 0.

Now, it can be seen that the L.H.S. is even and the R.H.S. is odd.

Hence there is contradiction and log 2 is irrational.

Hope it helps you!!